What determines colours? What is motion?

All colours in nature derive from the fine
structure constant 1/137.035 999 1(1). This is the most famous unexplained number
in nature. What determines its value? All motion in nature
is described either by quantum theory or by Einstein's general relativity,
two theories that contradict each other. How can they be unified in a
final theory?

If you enjoy exploring ideas and checking them against the real
world, you might like this volume. It first explains why the past
proposals for a final, unified theory of physics – the so-called
'theory of everything' – have failed. Then, the text presents a
better proposal: a final theory called the strand model. This model
agrees with all experimental data known so far and makes clear, falsifiable
predictions. They are being tested in experiments around the world. The
strand model
– predicts the standard model of particle physics – and allows
no alternative or extension, – is based on one simple
fundamental principle – and thus is 'beautiful', –
predicts general relativity – and allows no alternative or extension,
– predicts quantum theory – and allows no alternative or
extension, – and solves the open issues of the standard model,
gravitation and cosmology, including the explanation of all fundamental
constants.
All these results follow naturally from one simple principle.
Prepare yourself for a roller coaster ride trough modern physics, and for
the excitement of solving one of the oldest physics puzzles known. This is
an adventure that leads beyond space and time – right to the limits
of human thought. For example, the adventure shows that the term
'theory of everything' is wrong, whereas 'final theory' is correct.

Fast reading: for a quick overview of the book, just read the
'summary' section in each chapter.

The colour pdf file with embedded animations, shown just below,
is free. If you want a paper version delivered to your
address, click one of the 'Buy' buttons at the top left of the page.

An appetizer: a simple unified theory

The text presents an approach to the final, unified theory of physics with
a simple basis but intriguing implications. The model is based on
featureless strands that form space, particles and horizons; the
model sums up textbook physics in a single fundamental principle: events
and Planck units are crossing switches of strands. The following image
illustrates it:

Surprisingly, this fundamental principle, which works in three
dimensions only, allows to deduce Dirac's equation (from the belt trick),
the principles of thermodynamics and Einstein's field equations (from the
thermodynamics of strand crossing switches). As a result, quantum theory
and general relativity are found to be low-energy approximations of
processes at the Planck scale. In particular, strands explain the entropy
of black holes (including the numerical factor).

As a further surprise, in the same approximation, the fundamental
principle yields the three gauge groups and the Lagrangians of
quantum electrodynamics, of the strong and of the weak interaction,
including maximal parity violation and SU(2) breaking. The three
Lagrangians appear as a natural consequence of the three Reidemeister
moves of knot theory. The strand model does not permit any further
interaction, gauge group or symmetry group. The strand model might even be
the first unified model predicting the three gauge interactions – and
the lack of other ones.

In QED, the strand model proposes a simple understanding of Feynman
diagrams and of Schwinger's formula for the anomalous magnetic moment of
the electron and the muon.

As a final surprise, the fundamental principle predicts three fermion
generations, the Higgs boson, and the lack of any unknown elementary
particles. The strand model thus predicts that the standard model is the
final description of particle physics. The quark model and the
construction of all mesons and baryons are shown to follow from strands.
In other words, tangles of strands and their crossing switches explain all
known elementary particles, all their quantum numbers, and the lack of any
other elementary particles. The strand model might be the first unified
model predicting the elementary particle spectrum.

A natural method for the calculation of coupling constants, particle
masses and mixing angles appears. So far, mass sequences, several mass
ratios, the weak mixing angle, the sequence and the order of magnitude of
coupling constants are predicted correctly. Again, the strand model
might be the first unified model allowing such calculations. More
calculations are under way; the volume is regularly updated.

The strand model thus fulfils a famous wish about the final theory of
motion: it fits on a T-shirt.
This wish is less frivolous than it looks, because it asks for a clear and
simple fundamental principle.

Enjoying physics

The final theory of physics on a T-shirt? Indeed. (To support the
project, you can buy the T-shirt
here.) The search for a unified description of all motion in nature is
fascinating – and a beautiful adventure. Numerous wonders of nature
are encountered, including unexpected and captivating views on determinism,
on induction, on the axiomatization of physics and on the mass gap in gauge
theories. The search is fascinating, but not more than that: unification
has no application in technology or in business and confers no power
whatsoever. Anybody who assigns to unification more importance than to a
riddle is already on the wrong track. Searching for unification is like
looking for a beautiful flower in a large field during a walk through the
countryside. The search is a pure pastime: it is just for enjoyment.

It is fun to find out how playing with strands at Planck scale
reproduces quantum theory, general relativity and the standard model,
including its gauge groups and its particle spectrum. Despite this
playfulness, the strand model should not be called 'spaghetti
model'. (And the model is not
related to loop quantum gravity nor to string theory.)

Like the previous volumes, the text reduces math to a minimum; it
entertains and surprises on every page. The text only presupposes
knowledge about the concepts of electric charge, particle, Lagrangian, wave
function, gauge symmetry, and space curvature. If
you need to learn about these topics, read the
previous five volumes of the Motion Mountain series; they provide an
introduction to these concepts – and to established physics in
general – with as little math and as much pleasure as possible.

Enjoy the reading!

The flow of the storyThe text starts by listing
all open issues in fundamental physics in the year 2000. They are given in
the table of the millennium issues below. The text
then discusses many incorrect approaches to solve these issues. To find a
better approach, modern physics is first simplified as much as possible.
The results of this simplification are used to deduce the general
requirements that any final theory must fulfil; the main ones are listed in the requirements table below. The requirements
also explain why the previous approaches failed. It is shown that the main
requirement is the extension of nature's constituents. Then the
strand model is introduced and discussed; it is shown, step by step, that
it satisfies each requirement, that it solves all open issues, and that it
agrees with all experimental data. In particular, the strand model is
based on Planck units, uses neither continuity nor discreteness as
fundamental concepts, and does not assume that points or sets exist at
Planck scale. The model has no free parameters, is unique and
unmodifiable, and works in three spatial dimensions only. However,
dimensionality is not a parameter, but a result of the model: other numbers
of dimensions are impossible. As required from any final theory, the
strand model makes definite experimental predictions, also
given below. The predictions are quite unpopular and contradict those
of other unification proposals, but so far, none is
falsified by experiment.

Discussion and blogs

Open issues in fundamental physics in the year 2000

This is the full list of questions that were unsolved in
fundamental physics in the year 2000, the so-called millennium
list of open issues. A correct description of nature must solve each
of these questions. Such a description then qualifies as a unified and
final theory.

OBSERVABLE

PROPERTY UNEXPLAINED IN THE YEAR
2000

α

1/137.0359991(1), the low energy value of the
electromagnetic coupling constant

αw (or θw)

the low energy value of the weak coupling constant (or
of the weak mixing angle)

αs, θCP

the
value of the strong coupling constant at one specific energy value and the
strong CP violation constant

mq

the values of the 6 quark masses

ml

the values of 6 lepton masses

mW

the value of the mass of the W vector boson

mH

the value of the mass of the scalar Higgs boson

θ12, θ13, θ23

the value of the three quark mixing angles

δ

the value of the CP violating phase for quarks

θ'12, θ'13, θ'23

the value of the three neutrino mixing angles

δ', α1, α2

the value of the three CP violating phases for
neutrinos

3 x 4

the number of fermion generations and of particles in
each generation

J, P, C, etc.

the origin of all quantum numbers of each fermion and
each boson

c, ħ, k

the origin of the invariant Planck units of quantum
field theory

3+1

the number of dimensions of physical space and time

SO(3,1)

the origin of Lorentz and Poincaré symmetry (i.e., of
spin, position, energy, momentum)

S(n)

the origin of particle identity, i.e., of permutation
symmetry

U(1)

the origin of the electromagnetic gauge group (i.e., of
the quantization of
electric charge, as well as the vanishing of magnetic charge)

SU(2)

the origin of weak interaction gauge group and its
breaking

SU(3)

the origin of strong interaction gauge group

Ren. group

the origin of renormalization properties

δW = 0

the origin of wave functions and of the least action
principle in quantum theory

W = ∫ LSM dt

the origin of the Lagrangian of the standard model of
particle physics

0

the observed flatness, i.e., vanishing curvature, of the
universe

1.2 ⋅ 1026 m

the distance of the horizon, i.e., the ‘size’ of the
universe

ρde = Λc4/(8πG) ≈ 0.5
nJ/m3

the value and nature of the observed
vacuum energy density, also called 'dark energy' or 'cosmological
constant'

(5 ± 4) x 1079

the number of baryons in the universe, i.e., the average
visible matter density in the universe

f0(1, ..., c. 1090)

the initial conditions for c. 1090 particle
fields in the universe (if or as long as
they make sense), including the homogeneity and isotropy of matter
distribution,
and the density fluctuations at the origin of galaxies

ρdm

the density and nature of dark matter

c, G

the origin of the invariant Planck units of general
relativity

δ ∫ LGR dt

the origin of curvature, of the least action principle
and of the Lagrangian of general relativity

R × S3

the observed topology of the universe

As shown in the text, the strand model proposes an answer to each of these
open issues. Each answer follows unambiguously from the single,
fundamental principle that strand crossing switches define the Planck
units.

Requirements for a final theory

Any final theory must fulfil certain requirements. The first half of the
text shows how each requirement follows from the expressions for the
Compton wavelength and for the Schwarzschild radius, i.e., when quantum
theory and general relativity are combined. The full list of requirements
that appear is given in the text. That list
can be summarized in the following way:

At the Planck scale and all other energy scales, the
final theory must describe nature, and in particular particles, space and
horizons, as made of extended constituents fluctuating in a
background.

In the final theory, the fluctuations of the constituents must explain
all observed examples of everyday, quantum and relativistic motion: the
fluctuations must describe all observations and experiments with maximum
precision, imply all concepts of physics and explain all fundamental
constants.

The full list of requirements appears only when quantum physics and
general
relativity are combined. The requirements and their details do not follow
from one theory alone. This makes the search for the final theory a
special challenge; in a sense, the requirements for the final theory
contradict quantum physics and also contradict general relativity. The
final theory must thus contradict each part of 20th century physics.

The second half of the text shows, step by step, that the strand model
fulfils the full list of requirements. In fact, the strand model is the
only present candidate for a final theory that fulfils them. In
addition, the strand model makes several predictions that can be tested
against observation.

Predictions of the strand model – from 2008/2009

All predictions (except the corrected one) of the strand model were made
before any experiment at the LHC in Geneva, or on neutrinos, on forbidden
muon decays, on electric dipole moments, on QCD, on dark matter searches,
or in astrophysics. The predictions that are typeset in bold characters
(and a few others) are unique to the strand model:

Nature has three spatial dimensions, three gauge symmetry groups
– namely U(1), SU(2) and SU(3) – and three generations of
quarks and leptons. These statements are related and follow from
topological arguments only.

No additional elementary particle will be discovered.
(For an update, see below.) The
unitarity of scattering for longitudinal
W and Z bosons is maintained at all energies.

Dark matter is a mixture of known elementary particles and black holes.
Dark matter detectors will not detect anything new.

Gauge couplings, particle masses, mixing angles and their running
can be calculated with help of knot, polymer or cosmic string simulation
programs.

All neutrinos have mass and differ from their antiparticles.
Neutrinoless double-beta decay will not be observed.

Hadron form factors can be calculated ab initio.

The light scalar mesons are mostly tetraquarks; knotted two-quark
states and knotted glueballs are ruled out.

The probable non-existence of glueballs needs a better argument.

The electric dipole moment of elementary fermions is at most of the
order of the Planck length times the elementary charge.

The quark mixing and the neutrino mixing matrices are unitary.

The coupling constants, particle masses and mixing angles are constant
in time.

There are only three fermion generations. The proton and the positron
charge are equal.

The highest chromoelectric (and chromomagnetic) field in nature is
given by the highest force divided by the colour charge; similar limits
exist for the weak interaction. The limits can be checked in neutron/quark
stars or other astrophysical objects.

No gauge groups other than those of the standard model exist in
particle physics. No form of GUT, technicolour or supersymmetry is valid.
No other interaction exists. Protons do not decay.

No quantum gravity effect will ever be observed – not counting the
cosmological constant and the masses of the elementary particles.

No deviations from QCD and almost none from the standard model appear for any
measurable energy scale. In particular, the strand model implies that
SU(2) is broken and P, C and CP are violated in the weak interaction, and
that SU(3), confinement and asymptotic freedom are properties of the strong
interaction. Longitudinal W
and Z boson scattering is slightly changed at LHC energies through
non-local and non-perturbative effects. (For an
update, see below.)

No deviations from quantum theory or quantum electrodynamics
appear for any measurable energy scale. The QED energy dependence of the
fine structure constant is reproduced.

No deviations from thermodynamics appear for any measurable
energy scale.

The universe's integrated luminosity is c^5/4G.

If the cosmological constant is nonvanishing, it decreases with
time.

If the cosmological constant is nonvanishing, minimal electric and
magnetic fields, a minimum force and a minimum acceleration exist.

No deviations from special or general relativity appear
for any measurable energy scale. No doubly or deformed special relativity
arises in nature.

There are maximal electric and magnetic fields in nature.

No deviations from electrodynamics appear
for any measurable energy scale.

The Planck values are the smallest measurable length and time
intervals, the Planck momentum and energy are the highest measurable values
for elementary particles. A maximum curvature exists and the generalized
indeterminacy principle holds. (As predicted by many.)

The highest force and power values measurable locally in nature are
c^4/4G and c^5/4G. (As shown by Gary Gibbons and several others.)

The smallest entropy in nature is of the order k. (As shown by
many.)

The quantum of action, hbar, is the smallest action value measurable in
nature. (As shown by Niels Bohr.)

The speed of light, c, is the highest energy speed measurable locally
in nature. (As shown by Hendrik Lorentz, Albert Einstein and
others.)

Status of the predictions and of the model

Summary and outlook of autumn 2014

The
strand model is a minimal unified theory of motion. To
falsify the strand model there are many possibilities: a single
observation that disagrees is sufficient, because all predictions follow
from a single principle. So far, no such falsifying observation is known,
and the T-shirt with the
fundamental principle describes correctly all known observations. In
addition, the strand model explains many observations that are not
explained by any other, competing model, such as the gauge groups,
parity violation, the number of fermion generations, the particle spectrum,
certain mass ratios, many mass sequences, and more. These results
encourage to proceed. To verify the strand model, however, there is
only one possibility: to calculate the constants of the standard model.
This project is under way; the first crude approximation yields a fine
structure constant value of 1/191, instead of the measured value
1/137.036(1). The result, possibly the first known estimate from first
principles, is not too disappointing. The remaining effort for these
computer calculations is estimated to be 2
man-years.

In the summer of 2014, a reader suggested that the tangles proposed so
far for the W and Z might be wrong, out of esthetical and consistency
reasons. His suggestion has good chances to be correct. This might
explain the crude values that were obtained so far for the fine structure
constant and the W/Higgs mass ratio. The strand model thus remains a
work in progress.

Detailed status on the Higgs of autumn 2014 –
with the lessons from a mistake

The two experiments at
the LHC in Geneva have observed a neutral boson with a mass around 125 GeV.
It has spin 0, positive parity, no composite particle seems to fit, and it
indeed seems to be elementary.

Assuming that the observed boson is indeed the Higgs boson - and there
is no reason to question this - the 'dirty
trick' candidate tangle shown on the left of Figure 85 on page 291 seems to
apply to it. The candidate tangle shown in that figure is part of the text
since it was published in 2009 and was always mentioned as possible Higgs
boson tangle. In 2009, it was argued that the candidate tangle could not
be correct and thus the lack of a Higgs was predicted. The discovery of
the Higgs boson asked for a check of those arguments. The check showed
that the arguments were wrong. Correcting the arguments, a more detailed
and improved prediction is possible:

– Assuming that the Higgs tangle on the left-hand side of Figure
85 on page 291 is correct, then the tangle predicts a Higgs with vanishing
charge, positive parity and being elementary. – That Higgs
tangle suggests a crude mass approximation for the Higgs boson of 109 GeV.
– Assuming that the Higgs tangle is correct, we have an
intuitive proposal for one of the mechanisms that influences mass values,
complementing tangle knottedness. – If only one standard-model
Higgs boson exists and if the tangle of Figure 85 is correct, the strand
model agrees with all data.– If only one standard-model Higgs
boson exists and if no strand configuration would be possible, then the
strand model is wrong. However, Figure 85 excludes this
possibility.– If several Higgs bosons exist or if the tangle of
Figure 85 does not apply, the strand model is in trouble.– If no
Higgs boson exists after all, the strand model is in trouble.–
The strand model continues to predict the lack of
supersymmetry.– In the case that effects or particles or
interactions beyond the standard model are observed, the strand model is in
trouble.

A longer evaluation is found in the text. After correction of the
mistaken prediction, there is no contradiction between experiment and the
strand model. The correspondence between the strand model and the standard
model can be tested both in future experiments and through additional
theoretical research. For example: in principle, other, so far overlooked
strand configurations may also be of importance in nature; such
configurations will be discussed in the text if they appear. Another
example: no experiment has found any hint for physics beyond the standard
model. In tabloid terms, the strand model predicts the so-called
'high-energy desert', also called the 'nightmare scenario': up to almost
the Planck scale, particle physics is
completely described by the standard model and by nothing else.

Experiment and theory on strands – status
of autumn 2014

So far, not a single
experimental result contradicts the predictions of the strand model
deduced from the fundamental principle, not even the most recent results
from the LHC at CERN, the Tevatron, or the many other particle experiments.
In particular, the results for the main aims of the LHC, namely to find the
Higgs, to find supersymmetry, to clarify dark matter and to search for the
new and unexpected, are exactly those that are compatible with the strand
model. The ATLAS and CMS experiments at LHC have confirmed the standard
model of particle physics up to an energy of 1 TeV, and found nothing new.
Neither experiment, nor any other, found supersymmetry, dark matter, hidden
dimensions nor anything else that is unexpected. Of course, upcoming
experiments, at the LHC and elsewhere, still have many possibilities to
falsify the strand model.

After the strand model was proposed, independent theoretical
investigations in general relativity and space-time confirmed various
ideas of the strand model. Examples are Botta Cantcheff's fluctuating
strings in space, Carlip's fluctuating lines in space, Verlinde's emergent
gravity, Kempf's model with both continuity and discreteness, and recent
cosmological models with time-dependent cosmological constant. In particle
physics, the strand model turned out to confirm unpopular older ideas
unknown to the author that are scattered through the research literature.
Examples are Weinberg's proposal that the standard model plus general
relativity is all there is, Susskind's speculations of black holes as
single wound-up strings,
and the 1980 paper
by Battey-Pratt and Racey deducing the Dirac equation from a tethered
ball.

The proposed tangles for the leptons, and those for the W and Z, might
need improvement. Future will tell.